You have me on that automation.
I am not sure that it is Actionable, but you could probably write a Script to do it, if your version of PS is late enough to support Scripts.
My normal workflow is to just do the rough layout, for each Button (Button Layer Sets), and then do my Alignment & Distribution, when I am done, Selecting the appropriate Buttons and their Layer Sets in the Layers Palette. Remember, the one that you Select first, will become the "baseline," for the others, so Select in the appropriate order, or things get wonky fast - have your History Palette open, or Ctrl+Z at the ready.
I would post the question to the PS - Scripting Forum, and some Scripting guru will let you know quickly, if what you want is possible. There are some crazy-smart folk there, and they have helped me out several times.
Good luck, and please let me know how it goes.